Black-Scholes Calculator
Price European call and put options using the Black-Scholes model. Enter the stock price, strike price, time to expiry, risk-free rate, and volatility to get theoretical option prices and the key Greeks.
The Black-Scholes model (developed by Fischer Black, Myron Scholes, and Robert Merton in 1973) is the foundation of modern options pricing. It calculates the theoretical fair value of European-style options, which can only be exercised at expiration.
The formula uses five inputs: stock price (S), strike price (K), time to expiration (T), risk-free interest rate (r), and volatility (sigma). The model assumes the stock follows a geometric Brownian motion with constant volatility and that markets are frictionless.
The Greeks
- Delta measures how much the option price changes when the stock moves $1. A call with delta 0.60 gains $0.60 when the stock rises $1.
- Gamma measures how fast delta changes. High gamma means delta is very sensitive to stock moves.
- Theta is time decay, the amount the option loses each day just from the passage of time. It accelerates as expiration approaches.
- Vega measures sensitivity to volatility. A vega of 0.15 means the option gains $0.15 per contract for each 1% increase in implied volatility.
The Black-Scholes model has limitations: it assumes constant volatility (real markets have a volatility smile), no dividends in the basic form (this calculator uses the extension for continuous dividends), and European-style exercise only. Despite these simplifications, it remains the industry standard starting point for options pricing.